Due to cold weather a $1\, {m}$ water pipe of cross-sectional area $1\, {cm}^{2}$ is filled with ice at $-10^{\circ} {C}$. Resistive heating is used to melt the ice. Current of $0.5\, {A}$ is passed through $4\, {k} \Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In ${s}$)

(Given latent heat of fusion for water/ice $=3.33 \times 10^{5}\, {J} {kg}^{-1}$, specific heat of ice $=2 \times 10^{3}\, {J}$ ${kg}^{-1}$ and density of ice $=10^{3}\, {kg} / {m}^{3}$

An electric kettle (rated accurately at $2.5\, kW$) is used to heat $3\, kg$ of water from $15\,^oC$ to boiling point. It takes $9.5$ minute. Then, the amount of heat that has been lost is

$50 \,gm$ ice at $0°C$ in insulator vessel, $50g$ water of $100°C$ is mixed in it, then final temperature of the mixture is (neglect the heat loss)

$10\; gm$ of ice cubes at $0\;^{\circ} C$ are released in a tumbler (water equivalent $55\; g$ ) at $40\;^{\circ} C$. Assuming that negligible heat is taken from the surroundings, the temperature(in $^o C$) of water in the tumbler becomes nearely $(L_f=80\; cal / g )$

A vessel contains $110\,\,g$  of water. The heat capacity of the vessel is equal to $10\,\,g$ of water. The initial temperature of water in vessel is $10\,^oC.$  If  $220\,\,g$  of hot water at  $70\,^oC$ is poured in the vessel, the final temperature neglecting radiation loss, will be ........ $^oC$

A geyser heats water flowing at a rate of $2.0 kg$ per minute from $30^{\circ} C$ to $70^{\circ} C$. If geyser operates on a gas burner, the rate of combustion of fuel will be $\dots \; g \min ^{-1}$

[Heat of combustion $=8 \times 10^{3} Jg ^{-1}$  Specific heat of water $=4.2 Jg ^{-1} \; { }^{\circ} C ^{-1}$ ]